First move object with rigid body physics, then animate manually
You can use the Rigid Body Tools panel available from the toolshelf. Just setup your objects as normal, select the one you want to manually animate after the simulation and hit Bake To Keyframes.
(In this example, I have a cube as the active object with its mass set to brick and the plane as a passive object)



A dialog will popup, select the start and end frames and optionally the frame step and hit OK.



Once this is done you should see the rigid body simulation keyframes for the object appear in the timeline from the start and end frame you specified. You can then select the object and manually animate from thereon and even tweak the baked keyframes if you want.